On algebraic and more general categories whose split epimorphisms have underlying product projections

2012/08/09 by James R. A. Gray, Gray, James R. A., Nelson Martins-Ferreira +1
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #math.CT

paper · pdf · doi:10.48550/arxiv.1208.2032

arxiv created 2012/08/09 · arxiv updated 2012/08/13

Abstract

We characterize those varieties of universal algebras where every split epimorphism considered as a map of sets is a product projection. In addition we obtain new characterizations of protomodular, unital and subtractive varieties as well as varieties of right omega-loops and biternary systems.

Related

• Semidirect products in Universal Algebra
• Internal precategories relative to split epimorphisms
• Nonsurjective epimorphisms in decomposable varieties of groups
• Products and coequalizers in pointed categories
• Characterizations of majority categories